The SOR iterative method for new preconditioned linear algebraic systems

Abstract

Over the years, a good number of preconditioners have been introduced to improve the convergence of Iterative methods for solving linear systems. A common feature of most of these preconditioners is that the preconditioning effect is restricted to only certain entries of the coefficient matrix. In an effort to address this drawback, a new preconditioner is proposed; the effect of its application is observed on every entry of the coefficient matrix; in particular, the preconditioner eliminates the last entry on the leftmost column and scales down every other entry. Convergence and comparison theorems of the resulting preconditioned iteration technique are advanced and established. Simulated solutions of sample numerical examples via Maple 2019 Computer Algebra System are presented. It reveals that the proposed method converges faster than the SOR as well as other preconditioned iterations in literature.